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     "source": [
      "# $\\ell_1$ trend filtering\n",
      "\n",
      "A derivative work by Judson Wilson, 5/28/2014.<br>\n",
      "Adapted from the CVX example of the same name, by Kwangmoo Koh, 12/10/2007\n",
      "\n",
      "Topic Reference:\n",
      "\n",
      "* S.-J. Kim, K. Koh, S. Boyd, and D. Gorinevsky, ``l_1 Trend Filtering''<br>\n",
      "http://stanford.edu/~boyd/papers/l1_trend_filter.html\n",
      "\n",
      "## Introduction\n",
      "\n",
      "The problem of estimating underlying trends in time series data arises in a variety of disciplines. The $\\ell_1$ trend filtering method produces trend estimates $x$ that are piecewise linear from the time series $y$.\n",
      "\n",
      "The $\\ell_1$ trend estimation problem can be formulated as\n",
      "    \\begin{array}{ll}\n",
      "    \\mbox{minimize}   &  (1/2)||y-x||_2^2 + \\lambda ||Dx||_1,\n",
      "    \\end{array}\n",
      "with variable $x$ , and problem data $y$ and $\\lambda$, with $\\lambda >0$.\n",
      "$D$ is the second difference matrix, with rows \n",
      "    $$\\begin{bmatrix}0 & \\cdots & 0 & -1 & 2 & -1 & 0 & \\cdots & 0 \\end{bmatrix}.$$\n",
      "CVXPY is not optimized for the $\\ell_1$ trend filtering problem.\n",
      "For large problems, use l1_tf (http://www.stanford.edu/~boyd/l1_tf/).\n",
      "\n",
      "## Formulate and solve problem"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import cvxpy as cvx\n",
      "import scipy as scipy\n",
      "import cvxopt as cvxopt\n",
      "\n",
      "# Load time series data: S&P 500 price log.\n",
      "y = np.loadtxt(open('data/snp500.txt', 'rb'), delimiter=\",\", skiprows=1)\n",
      "n = y.size\n",
      "# Form second difference matrix.\n",
      "e = np.mat(np.ones((1, n)))\n",
      "D = scipy.sparse.spdiags(np.vstack((e, -2*e, e)), range(3), n-2, n)\n",
      "# Convert D to cvxopt sparse format, due to bug in scipy which prevents\n",
      "# overloading neccessary for CVXPY. Use COOrdinate format as intermediate.\n",
      "D_coo = D.tocoo()\n",
      "D = cvxopt.spmatrix(D_coo.data, D_coo.row.tolist(), D_coo.col.tolist())\n",
      "\n",
      "# Set regularization parameter.\n",
      "vlambda = 50\n",
      "# Solve l1 trend filtering problem.\n",
      "x = cvx.Variable(shape=(n,1))\n",
      "obj = cvx.Minimize(0.5 * cvx.sum_squares(y - x)\n",
      "                   + vlambda * cvx.norm(D*x, 1) )\n",
      "prob = cvx.Problem(obj)\n",
      "# ECOS and SCS solvers fail to converge before\n",
      "# the iteration limit. Use CVXOPT instead.\n",
      "prob.solve(solver=cvx.CVXOPT,verbose=True)\n",
      "\n",
      "print 'Solver status: ', prob.status\n",
      "# Check for error.\n",
      "if prob.status != cvx.OPTIMAL:\n",
      "    raise Exception(\"Solver did not converge!\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "     pcost       dcost       gap    pres   dres   k/t\n",
        " 0: -4.6668e-11 -1.0000e+00  1e+05  3e-01  4e-02  1e+00\n",
        " 1:  5.3971e-02 -6.9550e-03  1e+04  2e-02  3e-03  1e-01"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 2:  1.5513e-01  2.2236e-01  3e+03  7e-03  1e-03  1e-01"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 3:  1.4714e-01  2.3287e-01  6e+02  1e-03  2e-04  1e-01"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 4:  5.3138e-01  5.4713e-01  1e+02  2e-04  3e-05  2e-02"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 5:  5.1410e-01  5.3063e-01  1e+02  2e-04  3e-05  2e-02"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 6:  7.2454e-01  7.3795e-01  7e+01  1e-04  2e-05  1e-02"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 7:  8.0702e-01  8.1346e-01  3e+01  6e-05  1e-05  7e-03"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 8:  9.4942e-01  9.5462e-01  2e+01  5e-05  8e-06  6e-03"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 9:  1.0232e+00  1.0254e+00  1e+01  2e-05  3e-06  2e-03"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "10:  1.1802e+00  1.1812e+00  4e+00  8e-06  1e-06  1e-03"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "11:  1.2596e+00  1.2601e+00  2e+00  4e-06  7e-07  5e-04"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "12:  1.3502e+00  1.3504e+00  1e+00  2e-06  3e-07  2e-04"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "13:  1.3794e+00  1.3794e+00  3e-01  6e-07  1e-07  8e-05"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "14:  1.3956e+00  1.3956e+00  1e-01  3e-07  4e-08  3e-05"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "15:  1.3993e+00  1.3993e+00  4e-02  8e-08  1e-08  1e-05"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "16:  1.3994e+00  1.3994e+00  4e-02  8e-08  1e-08  1e-05"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "17:  1.4009e+00  1.4009e+00  1e-02  2e-08  4e-09  3e-06"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "18:  1.4012e+00  1.4012e+00  7e-03  1e-08  2e-09  2e-06"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "19:  1.4014e+00  1.4014e+00  2e-03  4e-09  6e-10  5e-07"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "20:  1.4014e+00  1.4014e+00  2e-03  3e-09  5e-10  4e-07"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "21:  1.4014e+00  1.4014e+00  2e-04  3e-10  5e-11  4e-08"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "22:  1.4014e+00  1.4014e+00  3e-05  6e-11  9e-12  7e-09"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "23:  1.4014e+00  1.4014e+00  2e-06  3e-12  5e-13  4e-10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "24:  1.4014e+00  1.4014e+00  2e-08  4e-14  6e-15  5e-12"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Optimal solution found.\n",
        "Solver status: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " optimal\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Results plot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "\n",
      "# Show plots inline in ipython.\n",
      "%matplotlib inline\n",
      "\n",
      "# Plot properties.\n",
      "plt.rc('text', usetex=True)\n",
      "plt.rc('font', family='serif')\n",
      "font = {'family' : 'normal',\n",
      "        'weight' : 'normal',\n",
      "        'size'   : 16}\n",
      "plt.rc('font', **font)\n",
      "\n",
      "# Plot estimated trend with original signal.\n",
      "plt.figure(figsize=(6, 6))\n",
      "plt.plot(np.arange(1,n+1), y, 'k:', linewidth=1.0)\n",
      "plt.plot(np.arange(1,n+1), np.array(x.value), 'b-', linewidth=2.0)\n",
      "plt.xlabel('date')\n",
      "plt.ylabel('log price')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "<matplotlib.text.Text at 0x10e95aad0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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X+Oijj9CyZUu0a9cO9vb2SEhIwNix23DsmA1SUsqjWTNg714ZqlZNg6WlJQBgz549qFat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       "text": [
        "<matplotlib.figure.Figure at 0x10c884c50>"
       ]
      }
     ],
     "prompt_number": 2
    }
   ],
   "metadata": {}
  }
 ]
}